A suburb with a population of 20,000 is begining to undergo rapid housing development, and is experiencing failure of its current individual household septic tank disposal system. The suburb has decided to build a sewage treatment plant to meet its needs for the next 20 years. The cost of the plant depends on the hydraulic flow, which is directly related to the populatation served. The suburb estimates its population 20 years from now as shown below:
Population | Probability |
20,000 ≤ population ≤ 25,000 | 0.30 |
25,000 ≤ population ≤ 30,000 | 0.30 |
30,000 ≤ population ≤ 35,000 | 0.40 |
Estimates are obtained on the cost of a wastewater treatment plant built today to meet the needs of three possible population levels as shown below:
Plant Capacity (persons) | Cost ($) |
25,000 | 1,200,000 |
30,000 | 1,400,000 |
35,000 | 1,550,000 |
It has been suggested, however, that money might be saved by building to a small capacity now and expanding the plant after ten years if population begins to exceed capacity at that time. Cost estimates, expressed in present value terms, are obtained for upgrading the size of the plant ten years from now, Theses are provided in third table.
Capacity (persons) | Upgraded Capacity (persons) | Present Worth Cost ($) | Probability |
25,000 | 30,000 | 190,000 | 0.20 |
|
| 230,000 | 0.50 |
|
| 270,000 | 0.30 |
25,000 | 35,000 | 320,000 | 0.25 |
|
| 390,000 | 0.55 |
|
| 410,000 | 0.20 |
30,000 | 35,000 | 130,000 | 0.30 |
|
| 190,000 | 0.50 |
|
| 210,000 | 0.20 |
Determine the size plant that the suburb should build today. Draw and label the decision free and state the optimal expected cost.
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